Set - Subset - Proper Subset

Set-Subset-Proper Subset
Citizen and Natural Born Citizen

This post is modified with corrections from a similar post on Mario Apuzzo's blog on March 1, 2015 at 5:56 PM.

>> http://puzo1.blogspot.com/2015/02/what-do-president-obama-and-senator.html

<<>>

I've been looking at the previous discussion on Mario's blog about "natural born Citizen" and that proper subset is the "best answer" to Mario's question for the two neo-birther math experts, and his discussion with Bob, Bryan Olson and Ph.D. Mathematician Kevin/Slartibartfast on Cafe Con Leche Republicans, and now I understand the point of calling a "natural born Citizen" a proper subset of the "citizen" set, the "born" U.S. "citizen" set.

It looks like the essence of the proper subset issue is the distinction between two articles of the Constitution, the Article II singular U.S. citizenship "by" birth and the Amendment XIV dual U.S./foreign citizenship "at" birth. Extraneous but relevant, is the naturalized "citizen" with singular U.S. citizenship "by" oath "after" birth.

A couple of days ago* Mario had a comment on his blog about the comment he put on Cafe Con Leche Republicans about citizens "by" birth vs. "at" birth vs. "after birth," which I have expanded on, part of which is included after your "best answer" question.

Here is part of Mario's "by" vs. "at" comment:

" “By birth,” as applied to citizenship, refers to birth alone being sufficient to cause citizenship to occur. Under American common law, as confirmed by naturalization Acts of Congress, U.S. citizenship attaches to a child “by birth” without the need of any law to allow that to occur, when the child is born in the United States to U.S. citizen parents.

"A true natural born citizen becomes a natural born citizen because he or she does not need a naturalization Act of Congress or the Fourteenth Amendment to make him or her so. His or her birth in the United States to U.S. citizen parents makes him or her a natural born citizen. Hence, he or she becomes a citizen “by birth” alone and without the need of any law to make him or her so, and surely without the need of any naturalization in whatever form it may come.

"On the other hand, “at birth,” when applied to citizenship, refers to citizenship occurring at the moment of birth. ... To know what is necessary to occur for one to be a “citizen” of the United States “at birth,” we have to look to law which creates that status. That law is either the Fourteenth Amendment or Acts of Congress, which are the only sources of law that exist which create that status. ... unless one satisfies another one of Congress’s naturalization Acts or treaties which then would make one a citizen after birth.

"If one needs the benefit of a law in order to be a citizen , then one is not nor can one be a natural born citizen.

If one needs the benefit of a law in order to be a citizen,
["by" birth
or
"at" birth
or
"by" oath (natural law - naturalized)]
then one is not nor can one be a natural born citizen.
["by" birth [natural law - born]]

"Ted Cruz became a “citizen” of the United States “at birth” because a law provided that he could be one. That law, 8 U.S.C. Sec. 1401(g), is a naturalization Act of Congress. Without that law, he would not have been a citizen at all.

"Hence, it was not his birth alone that was sufficient to give him his birth status, which is the case for natural born citizens. Rather, it was Congress through its naturalization statute that considered him to be a citizen of the United States at birth."

* February 27, 2015 at 7:45 PM
( http://puzo1.blogspot.com/2015/02/what-do-president-obama-and-senator.html )

This is my application of the "by" birth vs. "at" birth distinction.

The U.S. Constitution
Two Types of "Persons"
“Citizens” and “Natural Born Citizens"

The U.S. Constitution knows two types of "persons"—“citizens” and “natural born citizens."

In the U.S. Constitution, WE the People gave the Congress authority to naturalize new citizens "at" birth and "by" oath [positive law naturalization]. It has naturalized "citizens" "by oath" by statute since the 1790 Naturalization Act. In addition to positive law statutes, Congress has naturalized "citizens" "at birth" by amendment (14th Amendment). The constitution's original 1787 Article 2 "natural born Citizen" by birth and at birth* designation and status has been reinforced as perpetual, not abrogated and repealed, but reinforced as perpetual by the 1868 14th Amendment language: "All persons born or naturalized...citizens of...". The "born or naturalized" words together are declarative positive law language, not natural law and positive law language, and the words refer to (1) the "citizen" who is born ** and (2) the "citizen" who by oath is naturalized. The "born" "citizens" of the 14th Amendment and the "naturalized" "citizens" by statute*** are itemized on my blog, and it will be clear after being itemized why ALL of the 14th Amendment and statute "citizens" are dual U.S./foreign citizenship "proper subsets" of the citizen "set," and "natural born citizen" in Article 2 is the ONLY "citizen" who is a singular U.S. citizenship "proper subset" of the citizen "set."

* Not "by" birth alone, but "by & at" birth together. The "natural born Citizen" phrase contains two elements, a natural law aspect and a positive law aspect. The natural law "natural born" entity, not a status, an entity, is "by birth", and the positive law "citizen" status, not an entity, a status, is given "at birth", not "by birth", but is given "at birth" and not at a later time by statute.

** In the 14th Amendment, the original intent of the two aspects of Article 2, natural law/positive law—"by birth and at birth"—are reinforced with the 14th Amendment declarative language suggesting, not "by birth and at birth" natural law and positive law but "at birth and by oath" positive law alone. The 14th Amendment "born" designation is declarative positive law language about what the "status" of the "person" is "at birth", just as "naturalized" in the same sentence is declarative positive law language about what the "status" of the "person" is "by oath" (naturalization). The framers of the 14th Amendment were declaring that whether a "person" is born OR naturalized under the Fourteenth Amendment, that "person" is at the very least, a born "citizen" of the U.S. and the "born citizen" has the same status as a naturalized "citizen" of the U.S. Both are "citizens" of the U.S. The "citizens" part is itemized later in this discussion about why "natural born Citizen" is a "proper subset" of "citizen."

*** (8 U.S.C. Sec. 1401(g) ) The text of this statute says that a child born on foreign soil, not U.S. jurisdiction on foreign soil, but foreign soil, is a "citizen" of the United States "at birth" and not "by birth."

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

For context about the previous set theory discussion on Mario's blog, first I include Mario's "best answer" question on June 13, 2014 at 9:28 AM to Slartibartfast (Kevin—Ph.D. Mathematician) and Dr. Conspiracy (Kevin Davidson—Masters of Science in Mathematics—the designation is from his About page at ObamaConspiracy.org).

The Set/Proper Subset "Best Answer" Question

Mario Apuzzo, Esq. Said...
Dr. Conspiracy,

I am directing this comment to you because I know that you are a mathematician and you have supporters who are also in that field.

I asked Slartibartfast on this thread:

Let us assume that you are a math student going for your Ph.D. in Mathematics at Obama World Institute of Mathematics. You are taking a multiple choice exam on set theory. You are instructed that for each question you are to provide only one answer which must be the best answer of the choices provided.

Here is one of the questions of the exam:

-1. Natural born citizens is:

-a. A subset of citizens.
-b. A proper subset of citizens.
-c. A superset of citizens.
-d. None of the above.

Please provide your answer.

=====

[Next is Ph.D. Kevin/Slartibartfast's answer—and a personal finger-wag at Mario.]

[Mario:] Here is his answer:

[Ph.D. Kevin:] And finally, your math question:

If multiple answers are allowed (i.e. the rules are "choose all correct answers),
this is a perfectly fine question
(and something I would expect in an undergraduate set theory course)
and the only correct answer is both "a" and "b".

If not, I would go to the professor and explain that both "a" and "b" were correct.

If the professor did not immediately recognize that I was correct (and could prove it),
then I would go to the Director of Graduate Studies or the Department Chair to make sure
that they understood that the guy (or gal) they had teaching set theory was going senile.

Seriously, there has never been a graduate student in mathematics, nor will there be, that doesn't understand this perfectly. What you are suggesting is like an English literature professor not knowing their ABCs.

I know that you just assume that everything I say is wrong, but you are making yourself look like a complete fool here. Once again, I can prove that you are demonstrably wrong and everything I've said is correct. I strongly suggest you quit talking about subjects where objective truths can be established---your dishonesty sticks out like a sore thumb.

=====

[Now Mario is again speaking to Dr. C./Kevin]

Like I said, I know that you are a mathematician. I also know that you have taken many multiple choice exams in your life and that during those exams, you followed the reasonable instructions that were given to you in answering the questions rather than argue with the instructor about them.

I am also sure that you experienced many exams in which you were instructed to provide the one (1) “best” answer to the question from the choices provided. So, I will ask you the same question that I asked Slartibartfast (stated above).

Please provide your one (1) “best” answer to the question from the four possibilities provided.

June 13, 2014 at 9:28 AM


Mario Apuzzo, Esq. Said...
Dr. Conspiracy answered my set theory question. Here is what he said:

"Mr. Apuzzo, not being a mathematician, doesn’t realize that on math tests, you aren’t asked to provide the “best” answer. Math isn’t about value judgments.

"Since Apuzzo doesn’t define “best,” the respondent has to guess the definition, which just leads to confusion and disputes.

"What I find interesting is that I think that even in this formally straightforward question, Apuzzo is trying to surreptitiously wave around his straw man named “Obots think all citizens are natural born citizens.”

"The way I reason the problem, I will answer:

"-b. A proper subset of citizens.

"I call this answer “best” because the other true statement (-a. A subset of citizens.) can be derived from answer “b,” making it the more useful response."

=====

Dr. Conspiracy is wrong in everything that he said except his answer to my question.
[...snip]
In any event, Dr. Conspiracy provided the correct answer.

Hence, we can see that Ph.D. Mathematician Slartibartfast is wrong again. He said the best answer was a. and b. when the “best” answer is only b., meaning that natural born citizens is a proper subset of citizens.

Here is Slartibartfast trying to save face at Dr. Conspiracy’s blog:

A proper subset (a mathematical “term of art”, so to speak) is a subset (another “term of art”) which does not include the entire set.

In math, all of the words mean something specific and unique. Doc’s response is that of a mathematician replying thoroughly and thoughtfully to an extremely inane question.

=====

[Mario continues]

You have got to love Slartibartfast, telling us that Dr. Conspiracy, as a mathematician, replied “thoroughly and thoughtfully” to an “extremely inane question.” I thought Slartibartfast was also a mathematician. After all, he told us that he has a Ph.D. in Mathematics.

Also, why would someone need to be “thoroughly and thoughtfully” when answering an “extremely inane question?” And if it was such an inane question, why would Slartibartfast provide a wrong answer to the question?

Here is more from Slartibartfast:

"It’s certainly a nice change from Mario’s perfidy…

"FYI—when you’re reading in “math”, every word is important and conveys a unique meaning. There are no extraneous or ambiguous terms (or you are making the equivalent of a grammatical error).

=====

[Mario continues]

Notice how Slartibartfast is trying to save face even harder, educating others just after just being proven by Dr. Conspiracy that he gave the wrong answer to the question. He also did not follow his own lecture when he answered my question.

Rather, he chose to argue with the instructor and even go to the Department Head in protest over the question and then insisted that the question had two answers and not one “best” answer.

Dr. Conspiracy did not buy into any of that nonsense because he saw the writing on the wall. He simply provided the correct answer.

So, what can we say about Slartibartfast, who tells us that will not be around for several days? (I guess things will cool off for him during his absence.) You be the judge.

June 13, 2014 at 3:25 PM

One More Comment by Dr. Conspiracy/Kevin Davidson

It’s a technical term in set theory:
A proper subset is a
subset that is
not equal
to the
set

So for example.
Orly Taitz is a citizen = set B
who is not a natural born citizen = set A
She is in the set (citizens) = set B
but not the subset (natural born citizens) = set A

I found this comment on Dr. C./Kevin's blog—June 13, 2014 at 1:05 pm.
( http://www.obamaconspiracy.org/2014/06/reply-to-mario-apuzzo-on-immoral-birthers/#comment-334117 )

"It’s a technical term in set theory: A proper subset is a subset that is not equal to the set.

"So for example. Orly Taitz is a citizen who is not a natural born citizen. She is in the set (citizens) but not the subset (natural born citizens).

"Put another way, “A is a proper subset of B” means:

"1) All the elements of A are in B
"2) At least one element of B is not in A.

"Every set is trivially a subset of itself, but not necessarily a proper subset."

Analysis and Application
Hey, I'm Not A Mathematician—So What Do I Know, Right?

Now for my "hey, I'm not a mathematician, so what do I know" analysis and application of the comments of the three set theory experts. The question is about the "best" answer, as asserted by original birther Mario, confirmed by "one-U.S.-citizen-parent-is-good-'nuf-for-POTUS-eligibility" neo-birther mathematician Dr. C./Kevin, although confirmed to the chagrin of his neo-birther mathematician friend Ph.D./Kevin.

The "best" answer is that "natural born Citizen" is a "proper subset" of the "citizen" set. The "best" answer is NOT both "subset" AND "proper subset." Yes, both are correct, but the "best" answer is that "natural born Citizen" is a "proper subset" of the citizen "set."

Next is a very brief definition of subset and proper subset from Mathinsight.org.

Mathinsight.org

Definition of subset
( http://mathinsight.org/subset_definition )

A set A is a subset of another set B if all elements of the set A are elements of the set B.

In other words, the set A is contained inside the set B.

The subset relationship is denoted as A["C"]B. [On the Mathinsight.org page, a symbol that looks like a "C" is between "A" and "B"—it means "contained inside"].

For example, if A is the set {diamond, heart, club, spade} and B is the set {diamond, pyramid, heart, club, spade}, then A is contained inside B but B is not contained inside A.

Since B contains elements not in A, we can say that A is a proper subset of B.

Proper subset definition
( http://mathinsight.org/proper_subset_definition )

A proper subset of a set A is a subset of A that is not equal to A.

In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

For example, if A = {1, 3, 5} then B = {1, 5} is a proper subset of A.
The set C = {1, 3, 5} is a subset of A, but it is not a proper subset of A since C = A.
The set D = {1, 4} is not even a subset of A, since 4 is not an element of A.

The Mathinsight.org definitions use {A} as the "set" symbol and {B} as the "proper subset" symbol, but the "best answer" {A} symbol for "proper subset" and the {B} symbol for "set" are Dr. C./Kevin's as found in his previous "technical term in set theory" comment, so I have maintained Kevin's symbols here for comparison and contrast continuity.

For a more thorough comparison and contrast analysis of "natural born Citizen" as a proper subset of the "citizen" set, I have expanded the original question from one proper subset element to eight: {A} {C} {D} {E} {F} {G} {H} {I}.

Now that I finally understand the Mathinsight.org definitions of set/subset/proper subset, and still not being a mathematician, my analysis starts with Marios's confirmation that new meaning neo-birther Kevin/Dr. Conspiracy gave the "best" answer when he chose "b" proper subset: "In any event, Dr. Conspiracy provided the correct answer."

I won't post my entire analysis and application of "natural born Citizen" as a proper subset here, but it can be read at my blog, U.S. Constitution: The Original Birther Document of the Union"*

* "natural born Citizen" is a Proper Subset of "Citizen" ( http://originalbirtherdocument.blogspot.com/2014/12/time-to-change-conversation.html ) .

[...big snip...]

Set Theory Conclusions—"What does THAT mean?"
Using set theory, there are at least four irrefutable conclusions.

Point #1
All "natural born Citizens" are citizens "by" birth, but none, zip, zero, zilch, absolutely NONE of the amendment 14 citizens "at" birth are "natural born Citizens" "by" birth.

Point #2
All statute naturalized citizens "at" birth (Sen. Ted Cruz, Sen. Marco Rubio, etc.) or "by" oath are citizens, and NOT "natural born Citizens" "by" birth.

Point #3
All citizens "by" birth (Gov. Sarah Palin, Gov. Scott Walker, Sen. Rick Santorum, Sen. Mike Lee, etc.) can NOT be Amendment 14 citizens "at" birth ALSO because "natural born Citizens" "by" birth do NOT need to be recognized as Amendment 14 "citizens" "at" birth.

Point #4
Finally, and of course, NONE of the statute naturalized citizens "by" oath can be "natural born Citizens" "by" or "at" or "after" birth, since they were born on foreign soil to zero U.S. citizen parents.

"THAT" is WHY "natural born Citizen" means ONLY singular U.S. citizenship derived ONLY "by" birth on U.S. soil ONLY to two U.S. citizen married parents.

Art
U.S. Constitution: The Original Birther Document of the Union
( http://originalbirtherdocument.blogspot.com/ )